Simplify the following expression and state the condition under which the simplification is valid. $k = \dfrac{p^2 - 16}{p - 4}$
Explanation: First factor the polynomial in the numerator. The numerator is in the form ${a^2} - {b^2}$ , which is a difference of two squares so we can factor it as $({a} + {b})({a} - {b})$ $ a = p$ $ b = \sqrt{16} = -4$ So we can rewrite the expression as: $k = \dfrac{({p} {-4})({p} + {4})} {p - 4} $ We can divide the numerator and denominator by $(p - 4)$ on condition that $p \neq 4$ Therefore $k = p + 4; p \neq 4$